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# If a is a zero of the polynomial p(x), then (x - a) must be a factor of p(x).

We will use the concept of the remainder theorem in order to find the required answer.

## Answer: Yes, if a is a zero of the polynomial p(x) then (x - a) is a factor of p(x).

Let us see how we will use the concept of the remainder theorem in order to find the required answer.

**Explanation: **

The remainder theorem states that if any polynomial suppose that ax^{2} + bx + c is divided by (x - m) then on substituting the value x = m in the polynomial ax^{2} + bx + c we get the remainder. Now if the remainder is 0 then x = m is known as zero or root of the polynomial.

Now since the remainder is 0 then, (x - m) completely divides the polynomial ax^{2} + bx + c and we also know that if the dividend is completely divided by divisor then the divisor is one of the factors of the dividend.

### Hence, (x - a) is one of the factors of the polynomial p(x) if a is the zero of the polynomial.

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